Blender Cycles: uniform position-based colors?
This is just a response to mark this question as answered. The user Gorgious linked a video which showed the solution: youtu.be/05HFa3jNBH0?t=24

The trick seems to be to switch to top-down, orthographic view, then project a UV map from view, shift the UV map over the desired part of the texture, then select 'individual origins' and scale the UV map projections of each object waaaaay down. Done =)

Thanks, Gorgious!